Yeah, once you get to 1024, if you make a mistake and have to make an orphan 2 or 4, you pretty much know you're hosed. Maybe if you can keep at one you can still do it.
The "corner and avoid using up" strategy was what I came up with after a lot of playing earlier this week. Avoid trapping "lower" (relative to what else you have) on the board nearby your big guns at all costs. I found simultaneously building two blocks, one above and one to the left (or right) of your big guy to work well. When it's time to combine, it's usually pretty easy to line them up, then you're always building directly next to the big one in the corner. Also avoid having intermediate values, they just take up space. You want to have some 2s or 4s and the rest of the blocks be your maximums aside from the biggest.
Final tip is not to overzealously match pairs. You know that either a 2 or 4 will be appearing. If matching a pair will end up causing (or risking) that 2 or 4 getting trapped between two 256s or something, it's a bad move.
Got to 2048 and quit. Or I'd still be playing now. It also works great on mobile
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